German Offenlegungsschrift 3,148,939 discloses a method of fabricating reinforcement bodies for concrete structural parts, in which method cylindrical wire baskets for reinforcing ferroconcrete pipes are connected to one another by web wires. The cylindrical wire baskets are first supported with a horizontal axis in such a way that the axes of the wire baskets first of all do not coincide and the wire baskets are thus not concentric. A spacer is then fed horizontally in the direction of the theoretical centre point of the reinforcement body to be fabricated and is welded to the wires of the cylindrical wire baskets. After the wire baskets have been appropriately turned upwards, the following spacers are welded in one after the other. In the process, the two wire baskets move further and further apart from their initial position, which is characterized by a common contact point, until the concentricity of the two wire baskets is obtained. In this fabricating method, the concentricity is obtained only after a sufficiently large number of spacers have been welded in, since only a large number of spacers distributed at the periphery are able to carry the weight of the inner or outer wire basket not supported by the rollers or the drum. This known procedure is not only relatively complicated but has in particular the disadvantage that the spacers as well as their weld locations on the wire baskets are subjected to considerable bending stress. In addition, the known procedure can only be applied to wire baskets which consist of complete circles but not to grid bodies of annular sections, for only wire baskets of complete circles are dimensionally stable in such a way that they can be worked without workpiece-dependent mechanisms and can be moved into a concentric position by simple turning after the spacers have been welded in.